Davydenko, striving to recapture the form that took him to world No.3 in 2006, seemed set for his first tournament win since 2011 but Gasquet hit back from 4-2 down in the second set to claw his way to an eighth ATP title.
After taking the second set tiebreak 7-4, second seeded Gasquet gained the upper hand and broke the 31-year-old's serve three times in the deciding set.
World number 10 Gasquet joins fellow Frenchmen Fabrice Santoro, Nicolas Escude and Jo-Wilfried Tsonga as winners of the title that Davydenko captured in 2010, when he beat Roger Federer and Rafael Nadal back to back.
At ATP Chennai, second seed Janko Tipsarevic of Serbia made the final after he beat Slovenia's Aljaz Bedene 4-6 6-2 6-2.
Tipsarevic will now face Roberto Bautista of Spain, who beat Benoit Paire 3-6 6-1 6-4 in the other semi-final.
2-Richard Gasquet (France) beat Nikolay Davydenko (Russia) 3-6 7-6(4) 6-3
Roberto Bautista (Spain) beat 5-Benoit Paire (France) 3-6 6-1 6-4
2-Janko Tipsarevic (Serbia) beat Aljaz Bedene (Slovenia) 4-6 6-2 6-2
1-Andy Murray (Britain) beat 5-Kei Nishikori (Japan) 6-4 2-0 (Nishikori retired)
Grigor Dimitrov (Bulgaria) beat Marcos Baghdatis (Cyprus) 6-3 5-7 7-6(5)